Discrete structures and algorithms for multiflow, facility location, and network design

2017 Fiscal Year Final Research Report

• Project/Area Number: 26330023
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: The University of Tokyo
• Principal Investigator: Hirai Hiroshi 東京大学, 大学院情報理工学系研究科, 准教授 (20378962)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 多品種フロー / 施設配置問題 / ネットワークデザイン / 離散凸解析 / 劣モジュラ最適化 / 多項式時間アルゴリズム

Outline of Final Research Achievements

In this research project, we developed a new theory of discrete structures across multicommodity flow, facility location, and network design problems in discrete optimization. In particular, we partially extended discrete convex analysis, which was a theory of discrete convex functions on the integer lattice, to more general discrete structures. Based on this theory, we developed combinatorial polynomial time algorithms to classes of multicommodity flow problems for which such good algorithms had not been known before. As an application, we provided a combinatorial 2-approximation algorithm to the node-multiway cut problem.

Free Research Field

離散最適化